Loop Models, Marginally Rough Interfaces, and the Coulomb Gas

Abstract

We develop a coarse-graining procedure for two-dimensional models of fluctuating loops by mapping them to interface models. The result is an effective field theory for the scaling limit of loop models, which is found to be a Liouville theory with imaginary couplings. This field theory is completely specified by geometry and conformal invariance alone, and it leads to exact results for the critical exponents and the conformal charge of loop models. A physical interpretation of the Dotsenko-Fateev screening charge is found.